Blocking on Twitter requires you to visit the profile page of the person you want to block. They will no longer be able to see your tweets in their feed or @ you. However, it's a somewhat hollow gesture unless you have made your Tweets "protected", meaning that people can only see your Tweets upon your approval of their request.
Otherwise, all of your tweets are public and anybody, even those without an account, can type twitter.com/yourusername into their browser and get the latest.
To block someone on Twitter, go to their Twitter profile, click the human silhouette drop-down next to the "follow" button and select "block".